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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 51 · 40 sums
TalentJR

The trick (Paravartya Yojayet): For ax + by = c and dx + ey = f: bottom = a×e − b×d. x = (c×e − b×f) ÷ bottom; y = (a×f − c×d) ÷ bottom. Special case ax + by = c, bx + ay = f: add the equations to get x + y, subtract to get x − y, then add and halve. Check your x and y in the first equation.

NameDateTime takenScore ___ / 40
  1. 1.8x + 4y = −64 and 4x + 8y = −44 →
  2. 2.7x + 3y = 52 and 3x + 7y = 28 →
  3. 3.9x + 8y = 102 and 8x + 9y = 102 →
  4. 4.5x + 2y = −36 and 3x − y = −15 →
  5. 5.x − 4y = 18 and 4x + 3y = 15 →
  6. 6.4x − y = −18 and 6x − 3y = −36 →
  7. 7.2x + 7y = 68 and 7x + 2y = 58 →
  8. 8.x + 3y = −2 and 4x + 6y = 4 →
  9. 9.x − 6y = 60 and 5x − 6y = 84 →
  10. 10.8x + 7y = 45 and 7x + 8y = 45 →
  11. 11.x + 4y = 1 and 4x + y = 34 →
  12. 12.6x + 8y = 10 and 8x + 6y = 32 →
  13. 13.6x + 4y = 50 and 5x − 6y = −33 →
  14. 14.x + 5y = 39 and 5x + y = 51 →
  15. 15.3x + 5y = 59 and 5x + 3y = 61 →
  16. 16.4x + 6y = 56 and 6x + 4y = 44 →
  17. 17.6x + 4y = 64 and 3x + y = 25 →
  18. 18.3x + y = 17 and 4x + 3y = 21 →
  19. 19.4x + 5y = −4 and 3x − 3y = −30 →
  20. 20.3x − 5y = 67 and 6x − 2y = 70 →
  21. 21.4x − 5y = −16 and 2x + 5y = 22 →
  22. 22.x + 8y = 53 and 8x + y = 46 →
  23. 23.7x + 3y = 22 and 3x + 7y = 38 →
  24. 24.9x + 3y = 78 and 3x + 9y = 66 →
  25. 25.4x + 4y = 12 and 2x + y = 2 →
  26. 26.8x + 5y = 17 and 5x + 8y = 35 →
  27. 27.3x + 5y = 2 and 5x + 3y = 30 →
  28. 28.5x − 6y = 82 and x + 2y = −6 →
  29. 29.x + y = 3 and 3x − 4y = −47 →
  30. 30.4x + 3y = 30 and 4x − 3y = 18 →
  31. 31.2x + 4y = 46 and 4x + 2y = 38 →
  32. 32.3x + 3y = 12 and 2x + 4y = 12 →
  33. 33.6x + 3y = −60 and x − y = −7 →
  34. 34.6x + 4y = 86 and 4x + 6y = 84 →
  35. 35.2x + 5y = −1 and 5x + 6y = 4 →
  36. 36.4x + 3y = −6 and 4x − y = 18 →
  37. 37.2x − 3y = 5 and 4x + 6y = 46 →
  38. 38.6x − 5y = 37 and 4x + y = 3 →
  39. 39.6x − 4y = −18 and 5x + 5y = −65 →
  40. 40.4x − 4y = −32 and 4x + 4y = −8 →

Answer key

  1. x = −7, y = −2
  2. x = 7, y = 1
  3. x = 6, y = 6
  4. x = −6, y = −3
  5. x = 6, y = −3
  6. x = −3, y = 6
  7. x = 6, y = 8
  8. x = 4, y = −2
  9. x = 6, y = −9
  10. x = 3, y = 3
  11. x = 9, y = −2
  12. x = 7, y = −4
  13. x = 3, y = 8
  14. x = 9, y = 6
  15. x = 8, y = 7
  16. x = 2, y = 8
  17. x = 6, y = 7
  18. x = 6, y = −1
  19. x = −6, y = 4
  20. x = 9, y = −8
  21. x = 1, y = 4
  22. x = 5, y = 6
  23. x = 1, y = 5
  24. x = 7, y = 5
  25. x = −1, y = 4
  26. x = −1, y = 5
  27. x = 9, y = −5
  28. x = 8, y = −7
  29. x = −5, y = 8
  30. x = 6, y = 2
  31. x = 5, y = 9
  32. x = 2, y = 2
  33. x = −9, y = −2
  34. x = 9, y = 8
  35. x = 2, y = −1
  36. x = 3, y = −6
  37. x = 7, y = 3
  38. x = 2, y = −5
  39. x = −7, y = −6
  40. x = −5, y = 3

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